HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #1 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

What is the area of the figure below?

 12

Possible Answers:

Correct answer:

Explanation:

To find the area of the figure above, we need to split the figure into two rectangles. 

12.5

Using our area formula, , we can solve for the area of both of our rectangles

            

           

To find our final answer, we need to add the areas together. 

 

Example Question #237 : Geometric Measurement: Understanding Concepts Of Area And Relating Area To Multiplication And To Addition

If the formula to find the area of the white section of the rectangle below is , what is the formula to find that area of the purple section? 

Screen shot 2015 11 04 at 3.54.29 pm

 

Possible Answers:

Correct answer:

Explanation:

Both the purple section and the white section have the same length, . The width of the purple section is . Thus the area formula for the purple section of the rectangle is .

Example Question #111 : Geometry

What is the perimeter of a figure with seven sides, four of which measure 9 inches, two of which measure 10 inches, and one of which measures a foot?

Possible Answers:

Correct answer:

Explanation:

Add the side measures, in inches (changing one foot to 12 inches):

Example Question #112 : Geometry

What is the perimeter of a right triangle with hypotenuse  and a leg of length ?

Possible Answers:

It cannot be determined from the information given.

Correct answer:

Explanation:

Using the Pythagorean Theorem, the length of the second leg can be determined.

We are given the length of the hypotenuse and one leg.

The perimeter of the triangle is the sum of the lengths of the sides.

Example Question #2 : How To Find The Perimeter Of A Right Triangle

Which of these polygons has the same perimeter as a right triangle with legs 6 feet and 8 feet?

Possible Answers:

None of the other responses is correct.

A regular decagon with sidelength one yard.

A regular octagon with sidelength one yard.

A regular pentagon with sidelength one yard.

A regular hexagon with sidelength one yard.

Correct answer:

A regular octagon with sidelength one yard.

Explanation:

A right triangle with legs 6 feet and 8 feet has hypotentuse 10 feet, as this is a right triangle that confirms to the well-known Pythagorean triple 6-8-10. The perimeter is therefore  feet, or 8 yards.

We are looking for a polygon with this perimeter. Each choice is a polygon with all sides one yard long, so we want the polygon with eight sides - the regular octagon is the correct choice.

Example Question #262 : Plane Geometry

The perimeter of the following trapezoid is equal to 23 cm. Solve for . (Figure not drawn to scale.)

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Possible Answers:

Correct answer:

Explanation:

The perimeter is equal to the sum of all of the sides.

Example Question #1 : How To Find The Perimeter Of Square

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Use this image for the following problem. 

What is the perimeter of the square in this picture?

Possible Answers:

Correct answer:

Explanation:

The question only is looking for a part of the picture, just the square. With squares, the rule is that all the sides are equivalent, meaning the same lengths and all angles are right angles. 

Perimeter means adding up all the sides together. So we just need to add the lengths of the sides of the square. Uh oh, we only have one side that is listed.

Again, remember that with squares the sides are equivalent, and we know one side is 5 inches. We just need to take because a square has 4 sides. 

Our perimeter is .

Example Question #1 : Quadrilaterals

Sandy wants to put a border around her son’s nursery. If all four square walls in the room have the same width and use up feet of border, what is the length of one wall?

Possible Answers:

Correct answer:

Explanation:

When Sandy puts the border around her son's room, she will need enough to cover the perimeter.  Since the room has four walls equal in length, we know that the room is a square.  The perimeter of a square can by found by adding all the sides together, or by multiplying the length of one side by 4.  This can be written as:

Since we know that Sandy used  feet of border, we know the perimeter is . We can now write an equation:

Now, in order to isolate the variable, we can divide both sides by four.

The left-hand side simplifies to:

The right-hand side simplifies to:

When we solve, we find that the length of each wall is .

 

 

Example Question #2 : Quadrilaterals

Find the perimenter:

Question_4

Possible Answers:

Correct answer:

Explanation:

The perimeter is equal to the sum of the length of all sides. Each side is equal to . Therefore, the perimeter equals:

Example Question #115 : Geometry

You are given equilateral triangle  and Rectangle 

with .

What is the perimeter of Rectangle  ?

Possible Answers:

Correct answer:

Explanation:

 is equilateral, so .

Also, since opposite sides of a rectangle are congruent, 

 and 

The perimeter of Rectangle  is 

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